European conference on liquid crystals 2019

Geometric frustration of Cholesteric Liquid Crystals (CLCs) is known to strongly influence the natural twisting of the constituent molecules, modifying the macroscopic configurations they tend to arrange in, minimizing the energy of the system. The eventual presence of external factors, i.e. electric/magnetic fields, leads to further modifications on the supramolecular ordering. In the static case, all these interactions can be encoded in the Frank – Oseen energy density, through additional contributions sorting their effects either in the bulk or on the boundaries of the system. It is in this framework that we analyze the equations describing the several isolated or extended and periodic structures arising in these systems and actually generated and observed in several experimental studies. In particular, from the Frank – Oseen theory for confined CLCs we derive the equations for Skyrmion-like structures and Helicoids in the presence of an external static electric field and we solve them both analytically or numerically. We point out the main features of the solutions, such as their topological properties, the effects of the anchoring or the electric field on the shape of the solutions or again the different disclinations they form at the boundaries because of the incompatibility of the anchoring conditions with the natural cholesteric twist. Furthermore, also with the aid of numerical relaxation methods for the energy density, we show how these solutions can arrange in periodic lattice configurations and we study the interactions arising among the lattice elements.